diff --git a/src/shared/copy.c b/src/shared/copy.c
index 6a5a52309aa..14b9b61d8a2 100644
--- a/src/shared/copy.c
+++ b/src/shared/copy.c
@@ -1610,13 +1610,11 @@ int reflink(int infd, int outfd) {
         if (r < 0)
                 return r;
 
-        /* FICLONE was introduced in Linux 4.5, so let's fall back to BTRFS_IOC_CLONE if it's not supported. */
+        /* FICLONE was introduced in Linux 4.5 but it uses the same number as BTRFS_IOC_CLONE introduced earlier */
 
-        r = ioctl(outfd, FICLONE, infd);
-        if (r < 0 && ERRNO_IS_NOT_SUPPORTED(errno))
-                r = ioctl(outfd, BTRFS_IOC_CLONE, infd);
+        assert_cc(FICLONE == BTRFS_IOC_CLONE);
 
-        return RET_NERRNO(r);
+        return RET_NERRNO(ioctl(outfd, FICLONE, infd));
 }
 
 assert_cc(sizeof(struct file_clone_range) == sizeof(struct btrfs_ioctl_clone_range_args));
@@ -1633,13 +1631,17 @@ int reflink_range(int infd, uint64_t in_offset, int outfd, uint64_t out_offset,
         assert(infd >= 0);
         assert(outfd >= 0);
 
+        /* Inside the kernel, FICLONE is identical to FICLONERANGE with offsets and size set to zero, let's
+         * simplify things and use the simple ioctl in that case. Also, do the same if the size is
+         * UINT64_MAX, which is how we usually encode "everything". */
+        if (in_offset == 0 && out_offset == 0 && IN_SET(sz, 0, UINT64_MAX))
+                return reflink(infd, outfd);
+
         r = fd_verify_regular(outfd);
         if (r < 0)
                 return r;
 
-        r = ioctl(outfd, FICLONERANGE, &args);
-        if (r < 0 && ERRNO_IS_NOT_SUPPORTED(errno))
-                r = ioctl(outfd, BTRFS_IOC_CLONE_RANGE, &args);
+        assert_cc(FICLONERANGE == BTRFS_IOC_CLONE_RANGE);
 
-        return RET_NERRNO(r);
+        return RET_NERRNO(ioctl(outfd, FICLONERANGE, &args));
 }